Antiferromagnetism andd-wave superconductivity in cuprates: A cluster dynamical mean-field theory

Abstract

We present a new approach to investigate the coexistence of antiferromagnetism and d-wave superconductivity in the two dimensional extended Hubbard model within a numerically exact cluster dynamical mean-field approximation. Self-consistent solutions with two non-zero order parameters exists in the wide range of doping level and temperatures. A linearized equation for energy spectrum near the Fermi level have been solved. The resulting d-wave gap has the correct magnitude and k-dependence but some distortion compare to the pure d x 2 −y 2 superconducting order parameter due to the presence of underlying antiferromagnetic ordering. 71.10dA microscopic theory of High-temperature superconducting cuprates (HTSC) is still far from the final understanding [1][2][3]. One of the most important recent experimental achievements was the discovery of pseudogap (PG) phenomenon above superconducting transition temperatures (T c ) [4] and existence of a sharp 41-meV resonance below T c related with some collective antiferromagnetic excitations [5]. Recent neutron scattering experiments [6] provide a new insight for the interesting problem on the origin of a condensation energy. The coexistence of an antiferromagnetism (AFM) and d-wave superconductivity (d-SC) in cuprate could be a natural way of discussing such different HTSC phenomena. This require a quantitative electronic structure theory including two different type of the order parameters: AFM and d-SC. Within such approach one can in principle analyzed the phase diagram of HTSC cuprate and interplay between antiferromagnetism and d-wave superconductivity [7].A minimal theoretical tool for cuprates consists of the two-dimensional Hubbard model [1]. The importance of including the realistic tight-binding spectrum obtained from the LDA-band structure analyses [8] was realized during the last years. Unfortunately, a most accurate Quantum Monte-Carlo (QMC) simulation of hole-doped 2d-Hubbard model has a difficulty to describe an interesting part of the HTSC phase diagram near 15% doping at the low temperature due to so-called sign-problem [9]. The perturbation theory of d-SC [10] ignore the vertex corrections in the strong correlation case of HTSC. Great progress in the theory of the interacting fermions results from the developing of the dynamical mean-field theory [11,12]. While the antiferromagnetic phase is easy to incorporate in the single-impurity DMFT-approach [12], the d-wave superconductivity requires a cluster generalization of DMFT. Different cluster-DMFT scheme have been proposed [12,13] and the recent application to the problem of the pseudogap in HTSC [14] have shown the efficiency of the cluster DMFT approach. The investigation of paramagnetic phase of two dimensional Hubbard model could be simplified using a translational symmetry [13], while the problem of a coexistence of AFM and dSC demands a broken-symmetry cluster calculation. This is equivalent to multi-orbital DMFT approach [15] and could be solved with QMC method [16].In this Letter we investigate the ...

Dynamical mean-field theory study of stripe order and d -wave superconductivity in the two-dimensional Hubbard model

“…In previous CDMFT studies [52,53,58] it has been assumed that the self-energy of each cluster is equal, producing a uniform d-wave superconducting state with the same density and same staggered magnetization throughout the lattice. In our case, we relax this assumption by considering larger unit 075112-2…”

“…Thus, on the one hand, we extend the single-site real-space DMFT calculations [62,63,65,66] to include d-wave superconductivity and, on the other, we extend the uniform plaquette DMFT approximation [52][53][54][55]57,58] to include the striped order. We find a wide region of coexistence between striped order and spatially modulated d-wave superconductivity, and analyze the behavior of the superconducting order parameter in the striped states.…”

“…It has been used to gain insight to the Mott transition both in the Hubbard model [49] and in real materials [50]. Since the initial realization [52] that the plaquette DMFT (meaning cellular DMFT [51] with a 2 × 2 cluster) can describe d-wave superconductivity, this approximation has been employed to study the competition and coexistence of superconductivity and magnetic order in the ground state [53,54], the effect of nearest-neighbor repulsion [55,56], and finite temperature energetics and critical temperatures of the superconductivity [57,58]. This approximation in its basic form cannot produce a striped state, since the 2 × 2 unit cell does not allow modulation of the magnetization across the lattice.…”

Towards ab initio Calculations with the Dynamical Vertex Approximation

“…54,55) A way to address non-local correlations and to keep, at the same time, the local correlations of DMFT are cluster extensions of DMFT such as the dynamical cluster approximation (DCA) 56) and cellular DMFT (CDMFT). 57,58) Here, a cluster of sites, or a coarse-grained Brillouin zone is embedded in a non-interacting DMFT-like bath instead of a single site in DMFT. This way, non-local correlations within the cluster are accessible.…”

On the (anisotropic) uniform metallic ground states of fermions interacting through arbitrary two-body potentials inddimensions

“…4 The superconducting order parameter in the cuprate compounds is generally considered to have the d x 2 −y 2 symmetry [11][12][13]. Note in passing that in practice the inter-planar coupling of the electronic degrees of freedom is capable of stabilizing a d-wave superconducting state at finite temperatures, such as obtained within the framework of the so-called 'cluster dynamical mean-field' approximation [40,41] (see also [42,43]). relevant range of parameters.…”